Final answer:
Expressions b) (−45)^3, d) 35−104, and e) (9.8)^2−102 evaluate to negative rational numbers since they either involve raising a negative number to an odd power or resulting from subtracting a larger number from a smaller one.
Step-by-step explanation:
You are asked to identify which of the following expressions evaluate to negative rational numbers: a) –(9)^4 b) –(45)^3 c) –(38)^2 d) 35–104 e) (9.8)^2–102. To determine if an expression results in a negative rational number, we must evaluate the expressions and consider the sign and the type of the output.
- a) (–9)^4: Raising a negative number to an even power results in a positive number, therefore this expression is not negative.
- b) (–45)^3: Raising a negative number to an odd power results in a negative number, making this expression a negative rational number.
- c) (–38)^2: Similar to a), raising a negative number to an even power gives a positive number, so this is not negative either.
- d) 35–104: Subtracting a larger number from a smaller one results in a negative number, making this a negative rational number.
- e) (9.8)^2–102: This requires calculating the exact values to see if the result is negative or positive.
To answer e), solve as follows: (9.8)^2 = 96.04; 96.04 – 102 gives a negative result, thus making it a negative rational number.
Therefore, the expressions that evaluate to negative rational numbers are b) (–45)^3, d) 35–104, and e) (9.8)^2–102. Remember, any negative number that can be expressed as a fraction of two integers (where the denominator is not zero) is a rational number.